Math Problem Statement

Find the mean

Find the samples standard deviation, s.

Complete the Relative Frequency column and the Cumulative Relative Frequency Column.

Find the first quartile.

Find the median.

Find the third quartile.

What percent of the students owned at least five pairs?

Find the 40th percentile.

Find the 90th percentile.

Find the mean, find the sample's standard deviation (s), complete the Relative Frequency column and the Cumulative Relative Frequency column, find the first quartile, find the median, find the third quartile, what percent of the students owned at least five pairs, find the 40th percentile, and find the 90th percentile.

Solution

Mean and Standard Deviation

  • Mean (X̄): 3.7753.775
  • Sample Standard Deviation (s): 1.2911.291

Updated Table (Relative Frequency and Cumulative Relative Frequency)

XFrequencyRelative FrequencyCumulative Relative Frequency
120.0500.050
250.1250.175
380.2000.375
4120.3000.675
5120.3000.975
600.0000.975
710.0251.000

Next, let's calculate the quartiles and percentiles.

  • First Quartile (Q1): This corresponds to the 25th percentile.
  • Median (Q2): This corresponds to the 50th percentile.
  • Third Quartile (Q3): This corresponds to the 75th percentile.

Let me compute these values now.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like to proceed with further clarifications or calculations manually? If you have any other questions, feel free to ask!

Here are some follow-up questions:

  1. How is the quartile calculated from a frequency distribution?
  2. What is the significance of standard deviation in data analysis?
  3. How do cumulative relative frequencies help in percentile calculation?
  4. Can you explain how the relative frequency is calculated?
  5. What methods can be used to find the median in a grouped frequency table?

Tip: Quartiles and percentiles divide the data into equal parts and are key for understanding data spread.

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Math Problem Analysis

Mathematical Concepts

Statistics
Frequency Distribution
Quartiles
Percentiles
Standard Deviation

Formulas

Mean: X̄ = Σ(X * f) / N
Sample Standard Deviation (s): s = sqrt[Σ(X - X̄)² * f / (N - 1)]
Relative Frequency: f / N
Cumulative Relative Frequency: sum of all previous relative frequencies

Theorems

Empirical Rule
Percentile Calculation
Quartile Calculation

Suitable Grade Level

Grades 10-12

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